Syllogisme is made of a particular Negatiue Maior and of an vniuersall Affirmatiue Minor directly concluding a particular Negatiue as thus Bo Some man is not a stone car But euery man is a sensible bodie do Ergo Some sensible bodie is not a stone The name of this Mood is Bocardo The sixt Mood is when a Syllogisme is made of an vniuersall Negatiue Maior and of a particular Affirmatiue Minor directly concluding a particular Negatiue as thus Fe No man is a stone ri But some man is a sensible bodie son Ergo Some sensible bodie is not a stone The name of this Mood is Ferison Thus you haue all the three Figures together with their Moods plainly set forth with examples CHAP. X. Of a Syllogisme expositorie ANd now because a Syllogisme expository is said to be a Syllogisme of the third Figure I thinke it most meete to giue you an example there of euen here sor I haue already defined the same before Yea I remember yee said it was expositorie when the proofe or meane terme is an Indiuiduum but if yee giue example I shall the better vnderstand it Let this then be your example to prooue some men to bee both Orators and Philosophers by a Syllogisme expositorie thus Cicero was an Orator but Cicero was a Philosopher Ergo some men are both Orators and Philosophers againe to prooue that some rich men are not wise thus Crassus was not wise but Crassus was rich Ergo some rich men are not wise thus you see that this kind of Syllogisme serueth to proue both affirmatiuely and negatiuely as it were by way of example CHAP. XI An obiection concerning the three Figures and Moodes belonging to the same TO what purpose serue so many figures and moodes sith the first figure and the foure first moodes belonging to the same are onely perfect yea and so perfect indeed as the Mathematicians in seeking out the truth of any probleme will vse none other because the first figure alone doth suffice to conclude all kindes of problemes whatsoeuer they be whereby it should seeme that the two other figures with their moodes be superfluous They be not altogether superfluous for as the first figure serueth chiefly and onely to conclude an vniuersal affirmatiue so the second figure serueth to conclude an vniuersal negatiue and the third figure to conclude both a particular affirmatiue and also a particular negatiue as you may perceiue very well by the examples before rehearsed neither be the fifteen vnperfect moodes so vnperfect but that they may easily be reduced vnto the foure perfect by one of these wayes heere following that is to say either by conuersion or by transposing of the premisses or else by a Syllogisme leading to impossibilitie of which three wayes of Reduction we come now to speake by which things it doth plainely appeare what difference there is betwixt a perfect and vnperfect Syllogisme for the perfect Syllogisme hath no need of these helpes to make the Conclusion manifest as hath been said before CHAP. XII Of Reduction and of the kindes thereof and also of the signification of certaine consonants in the words of Art seruing to Reduction WHat is Reduction Reduction here is none other thing but a declaration prouing or shewing the goodnes of an vnperfect Syllogisme by a Syllogisme of a perfect moode How manfold is such Reduction Two-fold for it is either offensiue or else by impossibility What is Reduction offensiue Reduction offensiue is when a Syllogisme is reduced to his perfection either by conuersion or by transposing the premisses or else by both at once What meane yee by transposing of the premisses for as touching conuersion ye haue spoken thereof before lib. 3. cap. 6. The premisses are said to be transposed when the Maior is put in the Minors place or contrariwise the Minor into the Maiors place What is Reduction by impossibilitie Reduction by impossibility is when the goodnesse of the Syllogisme is so proued as the aduersary denying the same must needs be brought to some absurditie as to confesse two Contradictories to be both true at once or some proposition to be false which he hath confessed before to be true or is manifestly true of it selfe But first we wil speake of Reduction offensiue and then of Reduction by impossibility and because that Reduction offensiue is done sometime by conuersion and sometime by transposition and sometime by both at once and againe that sometime one of the premisses somtime both and sometime no more but the Conclusion onely is conuerted and that sometime by simple conuersion and sometime by conuersion per accidens the Schoolemen for â—…asement of the memorie haue made eight of the Consonants besides the Vowels in the words of Art before mentioned to be significatiue and to declare how euery proposition ought to be reduced For first these foure Consonants b. c. d. f. with one of the which euery vnperfect moode doth begin doe shew that such vnperfect moodes ought to bee reduced into those perfect moodes which doe begin with the like letter as Baralipton Baroco Bocardo into Barbara Câ—…lantes Caesare Camestres into Celarent Dabitis Darapti Disamis Datisi into Darij Fapesmo Frisesomorum Felapton Ferison Festino into Darij Which be the other foure Consonants and what doe they signifie The other foure Consonants put betwixt the Vowels bee these s. p. m. c. where of s. signifieth simple conuersion that is to say that the Vowell which next before this Consonant is to be simply conuerted p. signifieth conuersion per accidens m. betokeneth transposition of the premisses c. in the latter end or midst of the moode betokeneth Reduction by impossibilitie as in Baroco and Bocardo Giue examples and shew how such Reduction is to be made First as touching reduction by conuersion Cesare is reduced into Celarent by simple conuersion of the Maior as this Syllogisme in Cesare Ce No tree is a sensible body which is reduced into Celarent thus sa But euery man is a sensible body which is reduced into Celarent thus re Ergo no man is a tree which is reduced into Celarent thus Ce No sensible body is a tree la But euery man is a sensible bodie rent Ergo no man is a tree And Camestres is reduced into Celarent by simple conuerting the Conclusion and also by transposing the premisses as this Syllogisme in Camestres Ca Euery man is a sensible body which is reduced into Celarent thus mes But no tree is a sensible body which is reduced into Celarent thus tres Ergo no tree is a man which is reduced into Celarent thus Ce No sensible body is a tree la But euery man is a sensible bodie rent Ergo No man is a tree Festino is reduced into Ferio by simply conuerting the Maior as in this Syllogisme in Festino Fes No stone is a sensible body which is reduced into Ferio thus ti But some man is a sensible body which is reduced into Ferio thus no. Ergo
and of the diuers kindes thereof WHat is a compound Syllogisme and how many kinds thereof bee there A compound Syllogisme is that which is made of compound Propositions whereof as there be three sorts so they make three kindes of compound Syllogismes that is to say conditionall disiunctiue and copulatiue Of how many parts doth a compound Syllogisme consist Of three as well as a simple Syllogisme that is of the Maior containing two simple Propositions and of the Minor repeating the one part of the Maior and of the Conclusion concluding the other part of the Maior as in this example if this woman hath had a childe she hath laine with a man but shee hath had a childe Ergo she hath laine with a man How is the trueth of a compound Syllogisme to be sound out By reducing the same into a simple Syllogisme thus euery woman that hath had a childe hath laine with a man but this woman hath had a childe Ergo she hath laine with a man Are there no other kindes of compound Syllogismes No if you consider the order of concluding there be but three kindes or wayes that is to say conditionall disiunctiue and copulatiue but if you consider the varietie in vttering such Syllogismes you may make seuen sorts or wayes whereof three appertaine to the conditionall two to the disiunctiue and two to the copulatiue Which is the first way The first way is of the antecedent which being granted the consequent must needs follow both affirmatiuely and negatiuely Affirmatiuely thus if he be godly he is blessed he is godly therefore blessed negatiuely thus if he be not godly he shall not be blessed but hee is not godly Ergo hee is not blessed Which is the secondway The second way is of the Consequent which failing the Antecedent must also needs faile as thus If he be wise he is sree but he is not free Ergo not wise Which is the third way The third way is when by granting the Antecedent the Consequent faileth as thus If he be not wise he is wretched but he is wise Ergo not wretched Which is the fourth way The fourth way is when the former part of the maior Proposition disiunctiue being put the latter part is cleane taken away as thus He is either good or euill but he is good Ergo not euill Which is the fift way The fift way is when the former part of the Disiunctiue being taken away the latter part must needs stand as thus He is either good or euill but he is not good Ergo hee is euill for all Syllogismes Disiunctiue are made for the most part of parts repugnant whereof there can be no more but one true part Which is the sixt way The sixt way is by putting a Negatiue before the Coniunction copulatiue so as it maketh the Antecedent to stand and taketh away the Consequent as thus He is not both wise and wretched but he is wise Ergo not wretched Which is the seuenth way The seuenth way is when the Negatiue is placed in like manner before the Coniunction copulatiue but yet so as the Antecedent being taken away the Consequent doth stand as thus He is not both wise and wretched but he is not wise Ergo wretched CHAP. XVI Of a Consequent and by what meanes and rules the goodnesse thereof is to be knowne BVt sith the goodnesse of an Hypotheticall Syllogisme dependeth vpon the goodnesse of the Consequent it shall not bee amisse to treate heere of a Consequent and first to define what it is and to shew how it is diuided What is a Consequent A Consequent is a speech consisting of such parts as doe follow one another and are ioyned together with some rationall that is to say an inferring or imploying Coniunction as Ergo then therefore and such like How many parts are requisite in a Consequent Three that is the Antecedent the Consequent and the inferring Signe or Note for of these three parts euery Consequent consisteth How is it diuided Into two that is Good and Euill againe the good is diuided into two that is Formall and Materiall When is it said to be Formall When the Antecedent being true the Consequent doth necessarily follow thereof as when I say This woman hath had a child Ergo shee hath laine with a man When is it said to be Materiall When the Consequent doth not of necessitie but casually follow the Antecedent being true as Socrates walketh abroad Ergo it is faire weather Whereupon doth the goodnesse of a Consequent chiefely depend It dependeth not so much of the truth of the Antecedent and of the Consequent as of the necessarie connexion or knitting of them together and if the same be in forme of a Syllogisme it requireth also the precepts of Mood and Figure before taught to be obserued How else shall a man know whether a Consequent bee good or not By examining the same with the Maximes or generall rules of the places whereof some doe yeeld proofes or causes necessarie some probable and some only coniecturall What rules doe the Schoole-men set downe to know a good Consequent They set downe some more some lesse but Caesarius only reciteth two which are these The first is if a Consequent doth necessarily follow of his Antecedent then the contrary of the Antecedent must needs necessarily follow the contrary of the Consequent As for example because this is a good Cōsequent to say it is a man Ergo it is a sensible body it is a good Conquent to say it is no sensible body Ergo it is no man the reason thereof is because the contrary of the Consequent and the Antecedent cannot bee both true together but one of them must needs be false The second rule is that whatsoeuer followeth vpon a good Consequent must needs also follow vpon the Antecedent therof As for example if it be a good Consequent to say it is a man Ergo it is a sensible body ye may aswel say if it be a sensible body Ergo it is a substance and sith that a sensible body is a substance you may therefore aswel conclude that a man is a substāce To these rules you may adde also the third which is that of true things nothing can follow but truth but of false things sometime that which is false and sometime that which is true as hath bin said before and yet such truth followeth not by vertue of the false premises but because the cōclusion or Consequent is a true Proposition of it selfe As in this example Euery sensible body is a tree but euery Peare-tree is a sensible body Ergo euery Peare-tree is a tree CHAP. XVII Of a Syllogisme Demonstratiue HItherto we haue treated of a Syllogisme according to the first three of the foure diuisions thereof before mentioned for if yee remember well we said that according to the first diuision a Syllogisme is either Categoricall or Hypotheticall according to the second diuision eyther common or expository according to the third
intricate barbarous speeches then to serue to any other good purpose I thinke it better to passe them ouer with silence then to trouble your memorie therwith wherfore leauing them as things superfluous I minde now to treat of an hypotheticall or cōpound proposition of al the necessarie accidents therunto belonging CHAP. X. Of a compound or hypotheticall proposition WHat is a compound proposition It is that which consisteth of two or more simple propositions coupled together with some coniunction How manifold is it Threefold Conditionall Copulatiue and Disiunctiue When is it said to be conditionall When the coniunction If is set before any simple proposition as thus If it be a man it is a sensible body When is it said to be copulatiue When two simple propositions are ioined together with a coniunction copulatiue as God is true and man is a lier When is it said to be disiunctiue When two simple propositions are ioined together with a coniunction disiunctiue as thus Either it is day or night Of how many parts doth a compound proposition consist Of two that is of the antecedent and of the consequent Which call you the antecedent That which followeth next after the coniunction as thus If it be iustice it is a vertue here this speech If it be iustice is the antecedent and the rest of the speech that is to say it is a vertue is the consequent and so it should be though the words were contrarily placed as thus It is a vertue if it be iustice What things are to be considered in hypotheticall propositions These First whether they haue any quantitie or qualitie then whether any opposition equiualence or conuersion doe belong to them or not thirdly how to know the truth or falshood of euery such proposition be it conditionall copulatiue or disiunctiue And first as touching quantitie they haue none at all for quantitie is to be measured by signes vniuersall or particular which are only incident to the subiects of categoricall propositions but qualitie they haue in that they affirme or denie some thing by reason whereof there may be contradiction in hypotheticall propositions but it cannot bee properly said that they be either contrarie subcontrarie or subalternat for that they are without quantitie for want whereof they neither doe aptly admit opposition equiualence or conuersion but onely contradiction How is that Contradiction to be vnderstood By reason of affirmation or negation which as in simple propositions is to be taken on the behalfe of the verbe copulatiue and not of the subiect or predicate so in compound propositions it is to be taken on the behalfe of the coniunction hauing a negatiue set before it and yet not of euery coniunction but onely of that coniunction conditionall If whereof I cannot aptly giue you any example in our natiue tongue because it is contrarie to our naturall and vsuall speech to put a negatiue before the coniunction If and therefore I leaue to speake thereof any further and to say the truth it maketh but a strange kinde of speech in the Latine tongue and I beleeue is seldome vsed in any disputation as to say thus Non si animal est homo est or Non si lux est dies est both which are said to be negatiue speeches according to the rule before giuen because the negatiue is set before the coniunction si and by vertue thereof as the Schoolemen say maketh the whole proposition to be negatiue CHAP. XI Of the truth and falshood of Hypotheticall propositions and first of the Conditionall WHat is to be considered to know the truth or falshood of Conditionall Propositions First whether they be affirmatiue or negatiue for in the affirmatiues it sufficeth that the one part doth necessarily follow of the other as thus If it be a man it is a sensible body and it maketh no matter though the parts seuerally taken be both false so as the Cousequent be good as If a tree be a man a tree is a sensible bodie for though both these parts be false yet the Consequent conditionally is true for a conditionall Proposition hath no regard to the truth of the parts but onely that the Consequent may necessarily follow of the Antecedent How is the truth of the negatiue Proposition to be knowne By the Consequent for if the Consequent bee not rightly inferred of the antecedent then the negatiue is true as thus it followeth not that because a Lyon is a sensible body that therefore a Lyon is a man Of the truth and falshood of propositions copulatiue WHen is a copulatiue Proposition said to be true or false It is said to be true when both the parts bee true as when I say God is true and man is a lyar againe it is said to be false when either one part or both parts be false as when I say man is a sensible bodie and God is not a Spirit Here because the first part is true and the second part false the whole Proposition is said to be false It is said also to be false when both parts are false as thus Man is true and God is a lyar Heere both parts be false What kinde of propositions are wont to bee referred to this copulatiue Those which they call Temporall Locall by similitude and causall as of time thus When a penitent sinner prayeth then God heareth him Of place thus Where two or three are gathered together in the Name of the Lord he is in the midst of them By similitude thus As a man dealeth with his neighbour so will God deale with him Of the cause thus Because the Sunne shineth it is day And therefore certaine Aduerbes as these When Where Vntill so long as as so as for therefore because and such like haue the signification sometime of the Coniunction And and sometime of the Coniunction If Of the truth and falshoode of disiunctiues WHat belongeth properly to disiunctiue Propositions To consist of repugnant parts according to the signification of Coniunctions disiunctiue such as these bee vel or eyther or else and such like as eyther it is day or it is night whereof the one destroyeth the other for if the one be the other can not be and therefore they can not bee both true but they may be both false if there be any mean betwixt the two contraries as when wee say This woman is eyther white or blacke both these are false if she be browne which is a meane colour betwixt white and blacke But the later writers affirme the disiunctiue to bee true if any one or both of the parts bee true as thus Eyther a man is a sensible body or else a tree is a Substance and to bee false when both parts bee false as Eyther a man is true or God is a lyar The end of the third Booke of Logicke THE ART OF LOGICKE THE FOVRTH BOOKE CHAP. I. Of Places THough immediately after the Treatise of a Proposition the old men are wont to deale with
Some man is not a stone which is reduced into Ferio thus Fe No sensible body is a stone ri But some man is a sensible body o. Ergo Some man is not a stone Darapti is reduced from Darij by conuerting the minor per accidens as this Syllogisme in Darapti Da Euery man is a substance which is reduced into Darij thus rap But euery man is a sensible body which is reduced into Darij thus ti Ergo some sensible body is a substance which is reduced into Darij thus Da Euery man is a substance ri But some sensible body is a man j. Ergo Some sensible body is a substance Ferison is reduced into Ferio by simple conuersion of the minor as this Syllogisme in Ferison Fe No man is a stone which is reduced into Ferio thus ri But some man is a sensible body which is reduced into Ferio thus son Ergo some sensible body is not a stone which is reduced into Ferio thus Fe No man is a stone ri But some sensible body is a man son Ergo some sensible body is not a stone And so forth in all the rest according as the significatiue Consonants doe direct you CHAP. XIII Of Reduction by Impossiblitie HOw is Reduction by impossibilitie made By ioyning the Contradictorie of the concluon to one of the premisses and to dispose the same according to some one of the perfect moodes of the first figure in such sort as you may thereby make your Conclusion contradictory to the premisse which you left out and was granted by your aduersary whereby your aduersary is brought into an absurditie to con fesse two contradictories to be true both at once Giue examples As for example if your aduersarie would denie this Syllogisme in Baroco euery man is a sensible body but some tree is not a sensible bodie Ergo some tree is not a man then you may reduce it to the first Moode of the first figure which is Barbara by making the contradictorie of your Conclusion to be the Minor of your Syllogisme in this sort euery man is a sensible body but euery tree is a man Ergo euery tree is a sensible body which argument he cannot denie because hee hath granted the Minor to be true for if this Proposition some tree is not a man be false then this proposition euery tree is a man must needes be true for two Contradictories cannot bee both true at once and two true premisses must needes inferre a true Conclusion and note that according to the diuersitie of the figures the Contradictory of the Conclusion is diuersly disposed that is to say made either Maior or Minor accordingly for in all the Moodes of the second figure it must bee made the Minor the former Maior being still reserued and in the third figure it must be the Maior the former Minor being still reserued To which of the perfect Moodes is euery vnperfect Moode to bee reduced by impâ—…ssibilitie To know this it shall be needfull to learne first the vse of certaine words compounded of diuers sillables and inuented by the Schoolemen for this purpose Which be those words The words be these contained in this verse following nesciebatis odiebam letare Romanis whereof the first nesciebatis containing fiue sillables representeth the fiue vnperfect moods of the first figure odiebam hauing foure sillables betokeneth the foure vnperfect moodes of the second figure letare Romanis containing sixe sillables signifieth the sixe vnperfect moods of the third figure in all which words the foure vowels a. e. i. o. doe stil retaine their old significations before taught seruing here chiefly to shew the quantity and qualitie of euery Conclusion for euery vnperfect moode must bee reduced to that perfect moode of the first figure which hath such Conclusion as that vowel of the sillable representing that vnperfect mood doth signifie as for example in this word nesciebatis here you see that in the sillable nes representing the first vnperfect moode called before Baralipton the vowel e. signifying an vniuersall negatiue doth shew that this moode is to be reduced into Celarent whose conclusion is an vniuersall negatiue so as the order of the sillables in the word nesciebatis together with the signification of the vowels contained in the said sillables you may plainely perceiue that Baralipton is to be reduced into Celarent Celantes into Darij Dabitis into Celarent Fapesmo into Barbara Friselon into Darij The like obseruation and consideration is to be had in the other words representing the rest of the imperfect moodes of the second and third figure for odiebam appointeth Cesare to be reduced into Ferio Camestres to Darij Festino to Celarent Baroco to Barbara againe letare Romanis appointeth Darapti to Celarent Felapton to Barbara Disamis to Celarent Datisi to Ferio Bocardo to Barbara and Ferison to Darij whereof I giue you no examples because I would haue you to exercise your selfe in examining the former examples of the three figures and to see how you can reduce each vnperfect moode to his perfect moode by impossibilitie according to these short rules here set downe The Schoolemen after they haue taught the vse of the moodes and of reduction doe immediatly treat of a syllogisme made in oblique cases and also of the sixe habilities and three defects of a Syllogisme all which I willingly passe ouer with silence as things more curious then profitable for truely I know not whereto the Syllogisme made in oblique Cases doth serue more then for variety sake CHAP. XIIII Of Syllogismes made in oblique Cases and of the sixe Habilities and three defects of a Syllogisme WHat meane you by oblique Cases You learned in your Accidents that euery Noune hath sixe Cases that is to say the Nominatiue the Genitiue the Datiue the Accusatiue the Vocatiue and the Ablatiue wherof the Nominatiue is onely right and all the rest are called oblique as this is a Syllogisme made in oblique Cases euery drawing beast belongeth to man or is the beast of man but an oxe is a drawing beast Ergo an oxe belongeth to man or is the beast of man and as for the sixe habilities called sex potestates Syllogismi they are but meanes to proue the goodnesse of one Syllogisme by another or to shew which is more vniuersall or comprehendeth more then another or to conclude a trueth of false premisses which God wot is a sillie kinde of conclusion the best parts of which habilities are more easily learned by the rules and examples before giuen then by those that they set downe in their treatises touching the same Likewise the three defects are none other but Elenches or Fallaxes wherof there bee thirteene kindes set downe by Aristotle himselfe whereof we shall speake hereafter in their place so as they might say that there are thirteene defects as well as three and therefore leauing to trouble you with these things I minde here to treate of a compound Syllogisme CHAP. XV. Of a compound Syllogisme